I haven't been to a CiCi's, but I'm familiar with $5 Little Caesar's large 'Hot & Ready' pizza's. By any normal pizza standard, these are pretty awful. However, I wouldn't have to look very far to find worse at places who advertise themselves as being much better. And their new $8 Deep Dish pizzas are actually pretty good, IMHO.
But even a good pizza can be a really cheap thing. When I costed out my pizza using bulk pricing, my dough cost came to about 19 cents (food cost, not including labor). Tomato sauce is cheap, as well. I buy my Mozz & Provolone blend in bulk at a bit over $2/lb. I use about 10oz for a large pie, so let's call that $1.40 for cheese. So, say, $2 for a large cheese pizza.
At home, I use the Hormel pillow pack pepperoni for convenience - that's the budget killer right there. But I think with a proper deli slicer, the news would get much better. I'd like to think I could hit between $2.50-$2.90 for a large pepperoni pizza.
Now, I wouldn't want to sell that pizza for $5 (and it's certainly not a single serving one). That would be over 50% food cost, which would be insane. But if I could give you some lettuce and dressing and hope you'll eat only 1/3rd of a pie, that could be a winning proposition.